How would I solve this?

1. The position of a particle as it moves along the X axis is given for t > 0 byx = (t3 - 3t2 + 6t) m, where t is in 5. What is the position of the particle when it achieves its minimum velocity (after t = 0)? (10 points) 2. A commuter train travels between two downtown stations. Because the stations are only x=1000 m apart, the train never reaches its maximum possible cruising speed. During rush hour the engineer minimizes the travel interval At between the two stations by accelerating for a time interval Atl at 01 = 0.100 m/s2 and then immediately braking with acceleration 02 = 0.500 m/s2 for a time interval Atz. (a) Derive the expression to determine At; note that Atl and At; are not given (8 points) (b) Calculate At (2 points) %